I had a couple of conversations with Feynman when I first entered Caltech as
a freshman. He was always very attentive and helpful. This was in contrast to
Murray Gell-Mann who was not helpful to undergrads. I took a reading course from
Mathew Walker, which I first tried to get from Gell-Mann (he replied he didn't
read books), and I graded the then-grad math-physics course given by Walker when
I was a senior, a course which was put together by Feynman. I recall one very
stimulating special lecture I attended, I think as a junior, in which Feynman
delved into all kinds of side issues of various functions, e.g., roots of Bessel
functions, etc., and the punch-line at the end of the lecture was that all these
tangents miraculously led to the same number -- the Golden Mean.
When I was an Assistant Professor at SUNY, Stony Brook, I met Feynman again at a conference on partons in 1969, and I drove him back to the airport afterwards. He asked how I liked his lecture, e.g., relative to the others like C.N. Yang's. He was very appreciative of my remarks: I said that, unlike Yang who brought to bear a sophisticated arsenal of mathematics to develop some aspects of partons, his [Feynman's] lecture developed a coarse intuitive approach with minimal algebra -- but was an approach commensurate with the (lack of) knowledge of partons at that time, yet yielding more specificity of aspects of partons than the other lectures. I think that kind of approach was quintessential Feynman.
Shortly after that time, circa 1972, I met Feynman again with my long-time friend Hal Yura (one of Feynman's grad students, 3 years ahead of me at Caltech). I also got him interested in a project I was developing, on the physics of the brain. I was doing some experiments with neuroscientists at UCSD, which I started at SUNY SB, trying to gather some experimental data from noninvasive brain recordings, and I asked him if he would participate. He was excited and said he'd get back to me. So, Feynman decided to gather his own data, by not using any pencil or chalk for a couple of weeks to investigate his own brain. That led him nowhere, and he gave up on the project, stating "Thinking about thinking can make you crazy." I think that also was quintessential Feynman: He was quite suspicious of any phenomena that did not first have good experimental data or good tests for data. I admit that the experimental evidence was weak at that time, in the 1970's. However, I think that was a defect in Feynman's attitude to some research, in that that there are many phenomena that indeed clearly are based in some way in physics, and therefore deserve attention by physicists (even if they cannot be funded), but are currently as deficient in experiments as they are in theory.